Applying our segmentation method, 18 meshes of the Princeton Segmentation Benchmark [1]} are segmented
using \(k\)  columns of the affinity matrix \(W\) , where \(k=0.5\%,1\%,2\%,5\%,\%10\)  and \(\%25\)  of the total number \(n\)  of faces.
The Rand distance \(d_R\)  between the segmentations obtained for \(k\)  columns and the segmentation obtained with the
same distance for the whole matrix \(W\)  is computed. Three different metrics are considered, the geodesic,
the angular and the sdf metrics. For each of these metrics, in Figure REF  it is shown
the histogram of relative frequency of the Rand distance values between the segmentations obtained for \(k\)  columns
and the segmentation obtained with the same metric for the whole matrix \(W\) . This experiment shows that with
high probability, the segmentations with small number of columns \(k\)  are very close to the corresponding
segmentation obtained for the whole matrix \(W\) .
